Can someone help me Find the second derivative of xsquared(cos x) + 4sinx?

Question

For my work when i found the derivative for the first time i got 2xcosx - xsquared(sinx)+4 cos x... is this correct so far
^ above where the arrow is pointing and at xsquared(sin x) do i use the product rule to find the second derivative? because i did n i got this answer 2cosx-2(2xsinx)-xsquared(cosx)-4sinx but i donno if this is right? can someone please help me?

thank you i really appreciate it!!

Answer 1

For my first derivative I got...
2x cos x - x^2 sin x + 4 cosx which matches you.

For the second I got...
2 cos x - 4x sin x - x^2 cos x - 4 sin x which also matches you.

Looks like you are doing just fine. Hope I was of help.

Answer 2

y = x^2 cosx + 4 sinx

y' = x^2(-sinx) + (cosx) (2x) + 4 cosx

= - x^2 sinx + 2x cosx + 4 cosx

y'' = -x^2(cosx) + sinx (-2x) + 2x(-sinx) + cosx(2) + 4(-sinx)

= -x^2 cosx - 2x sinx - 2x sinx + 2 cosx - 4 sinx

= -x^2 cosx - 4x sin x + 2cosx - 4sinx

Answer 3

y = x² cos x + 4sin x
dy/dx = ( 2 x ) (cos x) - ( sin x ) ( x ² ) + 4 cos x
dy/dx = ( 2x + 4 ) cos x - ( sin x )( x ² )